A method of solution of the equations of classical gas-dynamics using Einstein’s equations

It is known that Einstein’s equations in general relativity provide explicit expressions for the density, pressure and velocity of a perfect gas in terms of the coefficients of the metric (the potentials) and hence in terms of the coordinates. Using orthogonal space-times, the expressions involve four potentials only between which consistency relations hold. It is shown how degeneration of the Einstein equations to Newtonian hydrodynamics provides general solutions of the equations of classical gas-dynamics for motions which may be either of constant or of variable entropy. The consistency relations are obtained in the general case. As an illustration, one-dimensional gas-dynamics are discussed and it is shown how the consistency relations are manipulated. The solution in which one or other of the Riemann variables is constant is obtained as a special case and motions of variable entropy are also attained.